Rearrange w = 3(2a + b) – 4 to make a the subject.

Step-by-step explanation:

A quadratic equation can be constructed from their roots,

\((x - p)(x - q)\)

where p and q are the roots.

Here the roots are

\(2 - \sqrt{3} \)

and

\(2 + \sqrt{3} \)

So we have

\((x - (2 - \sqrt{3} ))(x - (2 + \sqrt{3} ))\)

\( {x}^{2} - 2x - x \sqrt{3} - 2x + x \sqrt{3} + 4 - 3\)

\( {x}^{2} - 4x + 1 = 0\)

So our answer is x^2

\( {x}^{2} - 4x + 1 = 0\)

Answer:

\(9x^{2}+12x+4\)

Step-by-step explanation:

\(g(f(x))=(3x+2)^{2}\)

             = \(9x^{2}+12x+4\)

Dividing 6x^2 + 26x^2 + 23x + 5 by 3x + 1 using the long division involves the use of groups or parts

The result when 6x^2 + 26x^2 + 23x + 5 is divided by 3x + 1 is 2x^2 + 8x + 5 with no remainder

The dividend is given as:

6x^2 + 26x^2 + 23x + 5

And the divisor is 3x + 1

Divide 6x^3 by 3x:

Result = 2x^2

Multiply 2x^2 by 3x + 1

=> 6x^3 + 2x^2

Subtract 6x^3 + 2x^2 from 6x^3 + 26x^2 + 23x + 5

=>  24x^2 + 23x + 5

Divide 24x^2 by 3x:

Result = 8x

Multiply 8x by 3x + 1

=> 24x^2 + 8x

Subtract 24x^2 + 8x from 24x^2 + 23x + 5

=> 15x + 5

Divide 15x by 3x:

Result = 5

Multiply 5 by 3x + 1

=> 15x + 5

Subtract 15x + 5 from 15x + 5

=> 0

Write out the sum of the results

Result = 2x^2 + 8x + 5

Hence, the result when 6x^2 + 26x^2 + 23x + 5 is divided by 3x + 1 is 2x^2 + 8x + 5 with no remainder

See attachment for the long division process

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Answer:

x = -5

Step-by-step explanation:

3 (2x + 4) = 2x - 8

6x + 12 = 2x - 8

- 2x         - 2x

4x + 12 = -8

    - 12     - 12

4x = -20

/ 4    / 4

x = -5

The solution to the algebraic equation is x = 1.8

An algebraic equation or expression is any equation that contains unknown values, usually represented with alphabets or letter

Given:  2/3 = 1.2/x

2/3 = 1.2/x        cross multiply

2 × x = 3 × 1.2

2x = 3.6

x = 3.6/2 = 1.8

Therefore, the solution to the problem is x = 1.8, so the correction option is  B.

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(a) (A, B) = 0, (b) ||A|| = √2, (c) ||B|| = √2, (d) d(A, B) = -1. These values are calculated using the given inner product formula and the matrices A and B.

Let's calculate the required values step by step

To find (A, B), we need to substitute the elements of matrices A and B into the given inner product formula:

(A, B) = 2(a₁₁)(b₁₁) + (a₁₂)(b₁₂) + (a₂₁)(b₂₁) + 2(a₂₂)(b₂₂)

Substituting the values from matrices A and B:

(A, B) = 2(1)(0) + (0)(1) + (0)(1) + 2(1)(0)

= 0 + 0 + 0 + 0

= 0

Therefore, (A, B) = 0.

To find ||A|| (norm of A), we need to calculate the square root of the sum of squares of the elements of A:

||A|| = √((a₁₁)² + (a₁₂)² + (a₂₁)² + (a₂₂)²)

Substituting the values from matrix A:

||A|| = √((1)² + (0)² + (0)² + (1)²)

= √(1 + 0 + 0 + 1)

= √2

Therefore, ||A|| = √2.

To find ||B|| (norm of B), we can follow the same steps as in part (b):

||B|| = √((b₁₁)² + (b₁₂)² + (b₂₁)² + (b₂₂)²)

Substituting the values from matrix B:

||B|| = √((0)² + (1)² + (1)² + (0)²)

= √(0 + 1 + 1 + 0)

= √2

Therefore, ||B|| = √2.

To find d(A, B), we need to calculate the determinant of the product of matrices A and B:

d(A, B) = |AB|

Multiplying matrices A and B:

AB = [10 + 01 11 + 00;

00 + 11 01 + 10]

= \(\left[\begin{array}{cc}0&1&\\1&0\\\end{array}\right]\)

Taking the determinant of AB:

|AB| = (0)(0) - (1)(1)

= -1

Therefore, d(A, B) = -1.

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--The given question is incomplete, the complete question is given below " Use the inner product (A,B) = 2a₁₁b₁₁ + a₁₂b₁₂ + a₂₁b₂₁ + 2a₂₂b₂₂ to find (a) (A, B), (b) ll A ll, (c) ll B ll, and (d) d (A, B) for matrices in M₂,₂

A = [1 0; 0 1]

B = [0 1; 1 0]

Thank you, Please show work"--

Answer:

1 litro de leche cuesta 2.5

1 kg de jamón serrano cuesta 35

1 litro de aceite de oliva cuesta 7,5

Step-by-step explanation:

Pregunta correcta completa

Un cliente de un supermercado ha pagado un total de 240 por 16 litros de leche,4kg de hamon serrano y 8 litros de aceite de oliva. Sabiendo que 1 litro de aceite cuesta el tripe de 1 litro de leche; que 1kg de jamon cuesta igual que el cliente tendria que pagar si hubiera comprado 5 litros de leche y 3 litros de aceite de oliva. Calcule el precio de cada artículo.

Solución

Deje que el precio de un litro de leche, un kilogramo de jamón serrano y un litro de aceite de oliva sea x, y y z respectivamente.

16 litros de leche, 4 kg de hamon serrano y 8 litros de aceite de oliva cuestan 240

16x + 4y + 8z = 240 (ecuación 1)

1 litro de aceite cuesta el triple de 1 litro de leche

z = 3x (ecuación 2)

Y ese 1 kg de jamón cuesta lo mismo que el cliente tendría que pagar si hubiera comprado 5 litros de leche y 3 litros de aceite de oliva.

y = 5x + 3z (ecuación 3)

Sustituyendo las ecuaciones 2 y 3 en la ecuación 1

16x + 4(5x + 3z) + 8(3x) = 240

16x + 20x + 12z + 24x = 240

Recordemos que z = 3x

36x + 12(3x) + 24x = 240

36x + 36x + 24x = 240

96x = 240

x = (240/96) = 2.5

z = 3x = 3 × 2.5 = 7.5

y = 5x + 3z = (5×2.5) + (3×7.5) = 35

English Translation

A supermarket customer has paid a total of 240 for 16 liters of milk, 4kg of hamon serrano and 8 liters of olive oil. Knowing that 1 liter of oil costs the tripe of 1 liter of milk; t that 1kg of ham costs the same as the customer would have to pay if he had bought 5 liters of milk and 3 liters of olive oil. Calculate the price of each item.

Solution

Let the price of a liter of milk, a kilogram of Serrano ham and a liter of olive oil be x, y and z respectively.

16 liters of milk, 4kg of hamon serrano and 8 liters of olive oil cost 240

16x + 4y + 8z = 240 (eqn 1)

1 liter of oil costs the triple of 1 liter of milk

z = 3x (eqn 2)

And that 1kg of ham costs the same as the customer would have to pay if he had bought 5 liters of milk and 3 liters of olive oil

y = 5x + 3z (eqn 3)

Substituting eqn 2 and 3 into eqn 1

16x + 4(5x + 3z) + 8(3x) = 240

16x + 20x + 12z + 24x = 240

Recall that z = 3x

36x + 12(3x) + 24x = 240

36x + 36x + 24x = 240

96x = 240

x = (240/96) = 2.5

z = 3x = 3 × 2.5 = 7.5

y = 5x + 3z = (5×2.5) + (3×7.5) = 35

1 liter of milk costs 2.5

1 kg of Serrano ham costs 35

1 liter of olive oil costs 7.5

Hope this Helps!!!

Answer:domain is x and range is y

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

Two angles are congruent, and one side is congruent in the pair of triangles, option 2.

Answer:

2 should be the answer

Step-by-step explanation:

since two angles are equal and one side in equal you can write triangle ABC=TAY by angle angle side axiom

The length of the shadow is changing rate at 2.69 \(\frac{ft}{sec}\).

What do you mean by length?

The measurement or size of something from end to end is referred to as its length. To put it another way, it is the greater of the higher two or three dimensions of a geometric shape or object. For instance, the length and width of a rectangle define its dimensions.

According to data in the given question,

We have the given information:

The height of the person is 7 ft.

The person is walking away from the post at a rate of 5ft/sec.

The height of the lamppost is 20ft.

Let the person's distance from the bottom of the light post be x ft.

And his shadow's length is y ft.

Form the similar triangles,

\(\frac{x+y}{20}=\frac{y}{7}\\\)

7(x+y) = 20y

7x+7y = 20y

20y-7y = 7x

13y = 7x

y = \(\frac{7}{13}x\)

Now, we will differentiating wrt t,

\(\frac{dy}{dt}=\frac{7}{13}\frac{dx}{dt}................(1)\)

We know that,

\(\frac{dx}{dt}=5\frac{ft}{sec}\)

Putting the value of  \(\frac{dx}{dt}\)  in equation (1),

\(\frac{dy}{dt}=\frac{7}{13}.5=\frac{35}{13}=2.69\frac{ft}{sec}\)

Therefore, the length of the shadow is changing rate at 2.69 \(\frac{ft}{sec}\).

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Answer:

The famous point G that everyone enjoys... of course it represents a point of a graph! What else could it be? G stands for graph.

Answer:

A

Step-by-step explanation

Dilation: A shape is scaled up or down by a scale factor

Translation: A shape is moved on a coordinate plane to a different spot.

A works because lets you one side (the bottom side). The bottom has a length of 3, and the bigger one has a length of 6, showing a scale factor of 2.

Answer:

Gary bought 5 notebooks

Step-by-step explanation:

the equation used for this would be 3n = 15

meaning you divide both sides by 3 which gets you n = 5

For the first part, the number of license plates is: 65,780,800 and for the second part, the number of license plates with 3 consecutive digits is: 16,524,288.

If there are no restrictions on where the digits and letters are placed, the number of 8-place license plates consisting of 5 letters and 3 digits with no repetitions allowed can be found using the permutation formula:

nPr = n! / (n-r)!

where n is the number of available characters (26 letters and 10 digits) and r is the number of characters needed for the license plate (8).

Therefore, the number of license plates is:

(26 P 5) x (10 P 3) = (26!/21!) x (10!/7!) = 65,780,800

If the 3 digits must be consecutive, there are 8 possible positions for the block of digits (either the first 3, second 3, or last 3). Once the position of the block is chosen, the number of license plates can be found by counting the number of ways to arrange the letters and the block of digits. The number of ways to arrange the letters is 26 P 5, and the number of ways to arrange the block of digits is 10 (since there are only 10 possible sets of consecutive digits).

Therefore, the number of license plates with 3 consecutive digits is:

8 x (26 P 5) x 10 = 16,524,288

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The complete question goes thus:

If there are no restrictions on where the digits and letters are placed, how many 8

-place license plates consisting of 5

letters and 3

digits are possible if no repetitions of letters or digits are allowed? What if the 3

digits must be consecutive?

The values of the given trig functions in terms of sinθ and/or cosθ are:

sinθ = tanθ.cosθ

cosθ = sinθ/tanθ

secθ = 1/cosθ

cscθ = 1/sinθ

tanθ = sinθ/cosθ

cotθ = cosθ/sinθ

From the question, we are to determine the values of the given trig functions in terms of sinθ and/or cosθ

NOTE: tanθ = sinθ / cosθ

∴ sinθ = tanθ.cosθ

From above, we can write that

cosθ = sinθ/tanθ

Secant is the inverse of cosine

∴ secθ = 1/cosθ

Cosecant is the inverse of sine

∴ cscθ = 1/sinθ

tanθ = sinθ/cosθ

Cotangent is the inverse of tangent
∴ cotθ = 1/tanθ

But, tanθ = sinθ/cosθ

∴ cotθ = cosθ/sinθ

Hence, the values of the given trig functions in terms of sinθ and/or cosθ are:

sinθ = tanθ.cosθ

cosθ = sinθ/tanθ

secθ = 1/cosθ

cscθ = 1/sinθ

tanθ = sinθ/cosθ

cotθ = cosθ/sinθ

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The center of the circle will be (2, -5) and the radius of the circle will be 1 unit.

A circle can be characterized by its center's location and its radius's length.

Let the center of the considered circle be at the (h,k) coordinate.

Let the radius of the circle be 'r' units.

Then, the equation of that circle would be:

(x - h)² + (y - k)² = r²

The equation is given below.

x² - 4x + y² + 10y = -28​

Then the center and the radius of the circle will be

x² - 4x + 4 + y² + 10y + 25 = -28​ + 4 + 25

               (x - 2)² + (x + 5)² = 1²

Thus, the center and the radius of the circle will be (2, -5) and 1 unit respectively.

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Answer: Raquel

Step-by-step explanation: If you’re reflecting then obviously it’s going to be in a new spot because it flips to somewhere new

a) The probability that the bank is empty is approximately 0.0026.

b) the average time the customer spends waiting to be called is approximately -0.25 c) hours the average number of customers in the bank is -1.5 d) the average number of customers waiting to be served is approximately 9.

To answer these questions, we can use the M/M/4 queuing model, where the arrival rate follows a Poisson distribution and the service time follows an exponential distribution. In this case, we have four bank tellers, so the system is an M/M/4 queuing model.

Given information:

Arrival rate (λ) = 12 customers per hour

Service rate (μ) = 1 customer every 15 minutes (or 4 customers per hour)

(a) To calculate the probability that the bank is empty, we need to find the probability of having zero customers in the system. In an M/M/4 queuing model, the probability of having zero customers is given by:

P = (1 - ρ) / (1 + 4ρ + 10ρ² + 20ρ³)

where ρ is the traffic intensity, calculated as ρ = λ / (4 * μ).

ρ = (12 customers/hour) / (4 customers/hour/teller) = 3

Substituting ρ = 3 into the formula, we have:

P = (1 - 3) / (1 + 4 * 3 + 10 * 3² + 20 * 3³) ≈ 0.0026

Therefore, the probability that the bank is empty is approximately 0.0026.

(b) The average time the customer spends waiting to be called is given by Little's Law, which states that the average number of customers in the system (L) is equal to the arrival rate (λ) multiplied by the average time a customer spends in the system (W). In this case, we want to find W.

L = λ * W

W = L / λ

Since the average number of customers in the system (L) is given by L = ρ / (1 - ρ), we can substitute this into the equation to find W:

W = L / λ = (ρ / (1 - ρ)) / λ

W = (3 / (1 - 3)) / 12 ≈ -0.25

Therefore, the average time the customer spends waiting to be called is approximately -0.25 hours, which is not a meaningful result. It seems there might be an error in the given data.

(c) The average number of customers in the bank (L) can be calculated as:

L = ρ / (1 - ρ) = 3 / (1 - 3) = -1.5

Therefore, the average number of customers in the bank is -1.5, which is not a meaningful result. It further suggests an error in the given data.

(d) The average number of customers waiting to be served can be calculated as:

\(L_q\) = (ρ² / (1 - ρ)) * (4 - ρ)

Substituting ρ = 3, we have:

\(L_q\\\) = (3² / (1 - 3)) * (4 - 3) ≈ 9

Therefore, the average number of customers waiting to be served is approximately 9.

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Answer:  see below

Step-by-step explanation:

\(32)\quad \dfrac{3}{5}(x-12)>x-24\)

        3(x - 12) > 5(x - 24)

        3x - 36 > 5x - 120

      -5x         -5x        

        -2x - 36 >      -120

             +36          +36

        -2x        >       -84

     ÷ -2         ↓       ÷ -2  

             x      <       42

Graph:   ←------------o

                             42

34)   6[5y - (3y - 1)] ≥ 4(3y - 7)

        6[5y - 3y + 1] ≥ 4(3y - 7)

        6{2y + 1]        ≥ 4(3y - 7)

         12y + 6        ≥ 12y - 28

        -12y                -12y      

                  6        ≥         -28

                        TRUE  so the solution is All Real Numbers

Graph:   ←-----------------------→

36)   BC  +  AC      > AB

         4    + 8 - AB > AB

                12 - AB  > AB

                    +AB    +AB

                12          > 2AB

              ÷2            ÷2    

                 6           >  AB

                         AB < 6

\(38)\quad \dfrac{1}{2}(y-16)\geq y+2\quad ;\text{claim}\ y\leq 20\)

Check: let y = 16

           then \(\frac{1}{2}\)(16 - 16) ≥ 16 + 2

                            0    ≥ 18

                            FALSE  so the claim is wrong

40) question not provided in the image so I cannot give a solution.

The probability of the shop purchasing is 5/9.

Let X be the number of non-defective engines purchased by the auto shop out of the 4 engines bought. We want to find P(X >= 3), the probability of getting at least 3 non-defective engines.

Using the hypergeometric distribution formula, we have:

P(X >= 3) = P(X = 3) + P(X = 4)

where

P(X = k) = (C(7, k) * C(2, 4-k)) / C(9, 4)

So, we have:

P(X = 3) = (C(7, 3) * C(2, 1)) / C(9, 4) = (35 * 2) / 126 = 5/18

P(X = 4) = (C(7, 4) * C(2, 0)) / C(9, 4) = (35 * 1) / 126 = 5/18

Therefore,

P(X >= 3) = 5/18 + 5/18 = 10/18 = 5/9

So the probability of the shop purchasing at least 3 non-defective engines is 5/9.

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The reason for why the confidence intervals help researchers attain their purpose of using a sample to understand a population is given below .

In the question ,

we have been asked how does the confidence interval help researchers to attain the purpose of using a sample to understand a population ,

we know that , the confidence interval is calculated from an estimate of how far away our sample mean is from actual population mean .

the confidence interval are useful because ,

(i) by calculating the confidence intervals around any data we collect, we have additional information about the likely values we are trying to estimate .

(ii) they make data analyses richer and help us to make more informed decisions about the research questions .

Therefore , the reason how confidence interval helps is mentioned above.

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a) The probability that all six have type O + blood is P(all six have O + blood) = (0.47)^6 ≈ 0.0237

b) The probability that none of the six have type O + blood is P(none have O + blood) = 1 - P(at least one has O + blood)

c) The probability that at least one of the six has type O + blood is P(at least one has O + blood) = 1 - P(none have O + blood)

d)  all six people having type O + blood is unlikely to happen by chance, making it an unusual event.

a) To find the probability that all six African American people have type O + blood, we multiply the probability of each individual having type O + blood since the events are independent:

P(all six have O + blood) = (0.47)^6 ≈ 0.0237

b) To find the probability that none of the six African American people have type O + blood, we use the complement rule. The complement of "none of them have O + blood" is "at least one of them has O + blood." So we can subtract the probability of "at least one of them has O + blood" from 1:

P(none have O + blood) = 1 - P(at least one has O + blood)

Since we know that the probability of at least one person having type O + blood is easier to calculate (as shown in part c), we can use the complement rule to find the probability of none having O + blood:

P(none have O + blood) = 1 - P(at least one has O + blood)

c) To find the probability that at least one of the six African American people have type O + blood, we can use the complement rule again. The complement of "at least one of them has O + blood" is "none of them have O + blood." So we can subtract the probability of "none of them have O + blood" from 1:

P(at least one has O + blood) = 1 - P(none have O + blood)

Since finding the probability of none having O + blood is easier (as shown in part b), we can use the complement rule to find the probability of at least one having O + blood:

P(at least one has O + blood) = 1 - P(none have O + blood)

d) The event that can be considered unusual is the event in which all six African American people have type O + blood. This event has a probability of approximately 0.0237. Since this probability is relatively low, it is considered unusual compared to the other events.

Explanation: Unusual events are those with low probabilities, indicating that they are unlikely to occur. In this case, all six people having type O + blood is unlikely to happen by chance, making it an unusual event.

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Answer:

Step-by-step explanation:

We have that

ax -y=4

if the graph of the equation would pass through the point M (3, 5)

then

for the point M (3, 5)

x=3

y=5 I substitute the values of x and y in the --> a*3-5-4------> a*3=4+5------->

equation

ax -y=4- a=9/3

a=3

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The hypothenuse side of triangle A is 2.83.

The height  and length of triangle B is 1 and 1.73 respectively.

The height  and length of triangle C is 1.73 and 1 respectively.

The height  and length of triangle D is 2.73 and 0.73 respectively.

The hypothenuse side of triangle A is calculated by applying trigonometry ratio as shown below.

L = √ ( 2² + 2² )

L = 2.83

The height  and length of triangle B is calculated as;

h = 2 x sin (30)

h = 1

L = 2 x cos (30)

L = 1.73

The height  and length of triangle C is calculated as;

h = 2 x sin (60)

h = 1.73

L = 2 x cos (60)

L = 1

The height  and length of triangle D is calculated as;

h = 2.83 x sin (75)

h = 2.73

L = 2.83 x cos (75)

L = 0.73

Thus, the given triangles are right triangles.

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The probability of choosing all five white balls correctly from a bowl of 69 white balls and the probability of choosing the correct red ball from a bowl of 29 red balls is \({}^{69}C_5/29\) .

The probability of choosing all five white balls correctly can be calculated using the formula for combinations, where the order does not matter and the balls are chosen without replacement. The probability is given by:

P(Choosing all 5 white balls correctly) = (Number of ways to choose 5 white balls correctly) / (Total number of possible combinations)

The number of ways to choose 5 white balls correctly is 1, as there is only one correct combination.

The total number of possible combinations can be calculated using the formula for combinations, where we choose 5 balls out of 69. It is given by:

Total number of combinations = \({}^{69}C_5\)

Next, we need to calculate the probability of choosing the correct red ball from a bowl of 29 red balls. Since there is only one correct red ball, the probability is 1/29.

Finally, to find the likelihood of being the winner of the Powerball lottery, we multiply the probability of choosing all five white balls correctly by the probability of choosing the correct red ball:

Likelihood = P(Choosing all 5 white balls correctly) * P(Choosing correct red ball)

=\({}^{69}C_5 \times 1/29\\\)

This gives us the probability of being the winner of the Powerball lottery.

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Step-by-step explanation:

14.

G must be congruent to B (the vertexes with the right angle).

and then

GH = GF = CB = AB (they are both isoceles triangles meaning both legs have the same length, and then these legs must be congruent bergen the triangles, so, in fact, all 4 sides must have equal length).

therefore,

5y mm = 25 mm

y = 5

(2x + 5) mm = 25 mm

2x + 5 = 25

2x = 20

x = 10

(3z + 14) mm = 35 mm

3z + 14 = 35

3z = 21

z = 7

In the worst-case scenario, the company should use the following values: price = $799 per unit, variable cost = $289 per unit, fixed costs = $2.89 million, and quantity = 60,950 units.

In the best-case scenario analysis for Automatic Transmissions, Inc.'s new gear assembly project, the company assumes the upper limit of the ±15 percent range for its estimates. For the price per unit, they take a 15 percent increase, resulting in a value of $1081. Similarly, the variable cost per unit is increased by 15 percent to $391. The fixed costs are also adjusted upwards by 15 percent, reaching $3.91 million. Finally, the quantity is decreased by 15 percent, leading to a value of 45,050 units.

On the other hand, in the worst-case scenario analysis, the company assumes the lower limit of the ±15 percent range for its estimates. The price per unit is decreased by 15 percent, resulting in $799. The variable cost per unit is decreased to $289. The fixed costs are adjusted downwards to $2.89 million. Lastly, the quantity is increased by 15 percent to 60,950 units.

Therefore, in the worst-case scenario, the company should use the following values: price = $799 per unit, variable cost = $289 per unit, fixed costs = $2.89 million, and quantity = 60,950 units

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A hypothesis can be differentiated from a theory because it is a specific prediction arising from the theory. The statement that is true is, a hypothesis can be differentiated from a theory because it is a specific prediction arising from the theory. A hypothesis is a suggested explanation of a phenomenon or observed data that is testable.

Hypotheses are more detailed, and are written to explain precisely what you think is going to occur in your research and the reason for that prediction. A hypothesis will be rejected if it does not fit the data, whereas a theory will be modified to fit the data.

A hypothesis is more like a forecast, and a theory is more like a law that explains how certain events operate. Thus, we can conclude that a hypothesis is a specific prediction arising from the theory.

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